A Unified Probabilistic Monitoring Framework for Multimode Processes Based on Probabilistic Linear Discriminant Analysis

This article develops a novel probabilistic monitoring framework for industrial processes with multiple operational conditions. The proposed method is based on the probabilistic linear discriminant analysis (PLDA), which relies on two sets of latent variables, i.e., the between-class and within-class latent variables. In order to deal with the large within-class variations in multi-mode industrial processes, this approach modifies the original PLDA by introducing a separate within-class loading matrix for each operational mode and designs an expectation maximization (EM) algorithm to estimate the model parameters from the training samples. Mode identification for test samples is achieved by investigating the cosine similarity in the between-class latent variables and two monitoring statistics corresponding to within-class latent variables and the residuals are considered for fault detection. To diagnose the process fault, this article further develops a sparse probabilistic generative model based on PLDA for fault isolation. The enhanced performance of the proposed method is illustrated by applications to numerical examples and industrial processes.